# A chemist is making a solution that is to be 55% chlorine. He has one solution that is 40% chlorine and another that is 65% chlorine. He wants 100 liters of the final solution. How much of each should he mix?

##### 1 Answer

You need to mix **40 L** of 40% solution and **60 L** of 65% solution.

#### Explanation:

You know that the volume of the final solution is **100 L**. If

Now you need to focus on the chlorine content. Since the first solution is 40% chlorine, then for

The same can be said for the 65% solution

The final solution has a percent concentration of 55% chlorine, which means that it must contain

The second equation you can write will thus relate the amount of chlorine each solution contributes to the final solution

This is your system of equations

Use the first one to write

Now use this expression in the second equation to get the value of

This means that

So, if you mix **40 L** of a 40% chlorine solution with **60 L** of a 65% chlorine solution you will get 100 L of a 55% chlorine solution.